# [R] rootogram for normal distributions

S Ellison S.Ellison at lgc.co.uk
Mon Jan 17 15:54:36 CET 2011

```I was distracted enough by the possibility of hijacking hist() for this
to give it a go.

The following code implements a basic hanging rootogram based on a
normal density with hist() breaks used as bins and bin midpoints used as
the hanging location (not exact, I suspect, but perhaops good enough).
Extensions to other distributions are reasonably obvious.

S Ellison

rootonorm <- function(x, breaks="Sturges", col="lightgrey", gap=0.2,
...) {
h<-hist(x, breaks=breaks)
nbins<-length(h\$counts)
mu<-mean(x)
s<-sd(x)
normdens<-dnorm(h\$mids, mu, s)

plot.range <- range(pretty(h\$breaks))

plot(z <- seq(plot.range[1], plot.range[2], length.out=200),
dens<-dnorm(z, mu,s), type="n", ...)

d.gap <- min(diff(h\$breaks)) * gap /2

for(i in 1:nbins) {
rect(h\$breaks[i]+d.gap, normdens[i]-h\$density[i],
h\$breaks[i+1]-d.gap, normdens[i], col=col)

}

lines(z, dens, lwd=2)

points(h\$mids, normdens)

}

set.seed(17*13)
y <- rnorm(500, 10,3)
rootonorm(y)

>>> Deepayan Sarkar <deepayan.sarkar at gmail.com> 17/01/2011 05:06:54
>>>
On Sun, Jan 16, 2011 at 11:58 AM, Hugo Mildenberger
<Hugo.Mildenberger at web.de> wrote:
> Thank you very much for your qualified answers, and also for the
> link to the Tukey paper. I appreciate Tukey's writings very much.

Yes, thanks to Hadley for the nice reference, I hadn't seen it before.

> Looking at the lattice code (below), a possible implementation might
> involve  binning, not so?
>
> I see a problematic part here:
>
>   xx <- sort(unique(x))
>
> Unique certainly works well with Poisson distributed data, but is
> essentially a no-op when confronted with continous floating-point
> numbers.

True, but as Achim said, rootogram() is intended to work with data
arising from discrete distributions, not continuous ones. I see now
that this is not as explicit as it could be in the help page (although
"frequency distribution" gives a hint), which I will try to improve.

I don't think automatic handling of continuous distributions is simple
(because it is not clear how you would specify the reference
distribution). However, a little preliminary work will get you close
with the current implementation:

xnorm <- rnorm(1000)

## 'discretize' by binning and replacing data by bin midpoints
h <- hist(xnorm, plot = FALSE) # add arguments for more control
xdisc <- with(h, rep(mids, counts))

## Option 1: Assume bin probabilities proportional to dnorm()
norm.factor <- sum(dnorm(h\$mids, mean(xnorm), sd(xnorm)))

rootogram(~ xdisc,
dfun = function(x) {
dnorm(x, mean(xnorm), sd(xnorm)) / norm.factor
})

## Option 2: Compute probabilities explicitly using pnorm()

## pdisc <- diff(pnorm(h\$breaks)) ## or estimated:
pdisc <- diff(pnorm(h\$breaks, mean = mean(xnorm), sd = sd(xnorm)))
pdisc <- pdisc / sum(pdisc)

rootogram(~ xdisc,
dfun = function(x) {
f <- factor(x, levels = h\$mids)
pdisc[f]
})

-Deepayan

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